On a Z(3)-graded generalization of the Witten index

Abstract

We construct a realization of the algebra of the Z(3)-graded topological symmetry of type (1, 1, 1) in terms of a pair of operators D-1 : H-1 --> H-2, D-2 : H-2 --> H-3 satisfying [D1D1dagger, (D2D2)-D-dagger] = 0. We show that the sequence of the restriction of these operators to the zero-energy subspace forms a complex and establish the equality of the corresponding topological invariants with the analytic indices of these operators. (C) 2002 Published by Elsevier Science B.V.